Numerically controlled feeding apparatus having feeding error correcting system

ABSTRACT

A numerically controlled feeding apparatus having at least two linear feeding devices having intersected feeding directions includes a memory for storing beforehand representative correction vectors for representative instruction values indicating a predetermined number of reference feeding positions in the feeding space, each representative correction vector having information on deviation amount and deviation direction between a reference feeding position indicated by each of the representative instruction values and a real feeding position corresponding to each of the representative instruction value, a correcting unit for calculating a correction vector for an instruction value indicating any desired feeding position on the basis of a correction vector group of representative correction vectors for representative instruction values indicating plural feeding positions located in the neighborhood of the desired feeding position, and the instruction value indicating the desired feeding position, thereby to obtain a corrected feeding amount, and a control unit for controlling a feeding operation of the linear feeding devices on the basis of the corrected feeding amount.

BACKGROUND OF THE INVENTION

This invention relates to a numerically controlled feeding apparatus,and more particularly to a numerically controlled feeding apparatushaving a correcting system for a mechanical motional error of thefeeding apparatus.

A numerically controlled feeding apparatus has been used to feed variousmembers such as a machining member, a cutting tool, a plotter or thelike in one or higher dimensional direction. This numerically controlledfeeding apparatus includes, for example, a feeding table for supportingthe machining member or the like thereon, a guide surface for guidingthe feeding table therealong, a ball thread for moving the feeding tableon the guide surface; and other members. This type of feeding apparatushas been generally accompanied by a positioning or feeding error, whichfrequently occurs in a combined fashion of a pitch error of the ballthread, an unflatness error of the guide surface, an Abbe's error and soon.

In order to correct the positioning or feeding error as described above,there has been proposed a correcting device in which a difference in afeeding direction between an indicated position of a numerical positionindicating device and a real position of the machining member or thelike is stored as an error correcting value in a memory and then theerror correcting value is added to an instruction value representing theindicated position to thereby control the movement of the machiningmember. This correcting device is described in Japanese ExaminedPublished Patent Application No. 59-11125 and U.S. Pat. No. 3,555,254.

FIG. 1 is an explanatory diagram for explaining the error correctingvalue as described above, particularly in a case where an uniaxial orone-dimensional linear feeding apparatus is used. As shown in FIG. 1, afeeding table 102 for mounting a machining member or the like thereon isprovided in such a manner as to be movable on a guide surface 101, andfed along the guide surface 101 by a ball thread having a central axis104 in accordance with an instruction value from the numerical positionindicating device. In this case, a positioning or feeding control iscarried out at each of positions P1, P2 and P3 on the central axial 104of the ball thread whose direction corresponds to a feeding direction,in other words, the positioning is carried out at each of the stoppositions Q1, Q2 and Q3 of the machining member or the like (not shown)on a position estimation surface (ordinarily, a surface of an object 106to be machined).

As shown in FIG. 1, the stop positions Q1, Q2 and Q3 at which themachining member is really stopped on the estimation surface is notconsistent with indicated positions R1, R2 and R3 at which the machinemember is instructed, in advance, to be stopped because the pitch error,the Abbe's error, etc. occur. In this case, a difference in the feedingdirection between each of the stop positions Q1, Q2 and Q3 and each ofthe corresponding indicated positions R1, R2 and R3 corresponds to eachof positioning or feeding errors e1, e2 and e3 in the feeding direction.

The positioning errors e1, e2 and e3 occur in combined fashion withpitch errors p1, p2 and p3 of the ball thread, and the Abbe's errors a1,a2 and a3. The pitch error is caused by variation in pitch interval ofthe ball thread, and the Abbe's error is caused by deviation of a plane(A) vertical to the guide surface 101 from a plane B vertical to thefeeding direction due to unflatness of the guide surface), in otherwords, by a meandering movement of the feeding table 102 on the verticalplane B. The positioning or feeding errors e1, e2 and e3 are measuredbeforehand and stored as error correction values.

In an uniaxial (one-shaft) linear feeding apparatus, a correctingoperation is carried out by adding each error correction value to aninstruction value representing each of the stop positions Q1, Q2 and Q3.Further, in the biaxial (two-shafts) linear feeding apparatus, thecorrecting operation is carried out every feeding direction for eachshaft.

On the other hand, in the uniaxial linear feeding apparatus, the feedingerror also occurs in a direction (Y-axis) intersected (for example,perpendicular) to the feeding direction (X-axis) due to the meandering(unevenness or unflatness) of the guide surface 101. That is, themeandering (unflatness) of the guide surface 101 in a feeding direction(axis) causes not only a feeding error in the direction, but alsoanother feeding error in a direction intersected (for example,perpendicular) to the direction. In other words, a feeding operation ona feeding axis causes at least two feeding errors on the feeding axisand another feeding axis different therefrom (or intersected thereto).

In the conventional linear feeding apparatus having two or more feedingaxes (shafts) which are intersected to each other at an angle, a feedingerror on each feeding axis is independently corrected using a correctedfeeding amount with respect to only the feeding axis although thefeeding error on a feeding axis is caused by not only a feedingoperation on the feeding axis, but also a feeding operation on anotherfeeding axis, that is, the feeding errors on all the feeding axes arenot autoerrors which are independent of one another, but correlatederrors which are related to one another.

Accordingly, in the conventional numerically controlled feedingapparatus having at least two linear feeding devices whose feedingdirections are intersected to each other, a feeding error of one linearfeeding device which occurs in one feeding direction includes at leastone component of a feeding error of the other feeding device (forexample, an error component occurring on the Y-axis which is caused bythe feeding operation on the X-axis), so that a feeding error in afeeding direction has a complicated mechanical error. However, thiscomplicated mechanical error can not be completely corrected in theconventional feeding apparatus because each linear feeding devicecarries out a correcting operation for a feeding error (autoerror)thereof independently of the other feeding errors which are caused bythe other linear feeding devices.

SUMMARY OF THE INVENTION

An object of this invention is to provide a numerically controlledfeeding apparatus in which correlated feeding errors in all feedingdirections or axes can be completely and accurately corrected to therebyperform a feeding operation with high accuracy.

In order to attain the above object, according to one aspect of thisinvention, a numerically controlled feeding apparatus comprises memorymeans for storing representative correction vectors for representativeinstruction values indicating a predetermined number of referencefeeding positions in the feeding space, each representative correctionvector having information on deviation amount and deviation directionbetween a reference feeding position indicated by each of therepresentative instruction values and a real feeding positioncorresponding to each of the representative instruction value,correcting means for calculating a correction vector for an instructionvalue indicating any desired feeding position on the basis of acorrection vector group of representative correction vectors forrepresentative instruction values indicating plural feeding positionslocated in the neighborhood of the desired feeding position, thecorrection vector group being read out of the memory means, and theinstruction value indicating the desired feeding position, thereby toobtain a corrected feeding amount, and control means for controlling afeeding operation of the linear feeding devices on the basis of thecorrected feeding amount.

According to another aspect of this invention, a method for performing afeeding operation of a numerically controlled feeding apparatus havingat least two linear feeding devices while correcting an feeding error,comprises the steps of measuring beforehand and storing representativecorrection vectors for representative instruction values indicating apredetermined number of reference feeding positions in a feeding space,each representative correction vector having information on deviationamount and deviation direction between a reference feeding positionindicated by each of the representative instruction values and a realfeeding position corresponding to each of the representative instructionvalue, calculating a correction vector for an instruction valueindicating any desired feeding position on the basis of a correctionvector group of representative correction vectors for representativeinstruction values indicating plural feeding positions located in theneighborhood of the desired feeding position, and the instruction valueindicating the desired feeding position, thereby to obtain a correctedfeeding amount, and controlling a feeding operation of the linearfeeding devices on the basis of the corrected feeding amount.

BRIEF DESCRIPTION OF THE INVENTION

FIG. 1 is an explanatory diagram for explaining a feeding error andcorrecting the error in a conventional feeding apparatus;

FIG. 2 is a perspective view of one embodiment of a numericallycontrolled feeding apparatus according to this invention;

FIG. 3 is an explanatory diagram for showing a relationship between afeeding error and correcting vectors therefor when two linear feedingdevices are used;

FIG. 4 is a partly-enlarged view of the feeding areas as shown in FIG.3;

FIG. 5 is a block diagram for an error correcting device used in thenumerically controlled feeding apparatus according to this invention;and

FIG. 6 is a flowchart for showing an error correcting operation.

DETAILED DESCRIPTION OF THE INVENTION

A preferred embodiment of this invention will be described hereunderwith reference to the accompanying drawings.

FIG. 2 is a perspective view of one embodiment of a numericallycontrolled feeding apparatus according to this invention.

The numerically controlled feeding apparatus as shown in FIG. 2 is agantry type of cross-feeding (X,Y-feeding) apparatus. The apparatusincludes a machine bed 1 for mounting various members such as amachining head, a plotter or the like for performing a feedingoperation, a pair of Y-axis guide members 2 extending in a Y-directionwhich is fixedly mounted on the machine bed 1, and a ball thread 6 whichis rotatably mounted on the machine bed 1. The ball thread 6 is rotatedby a servo motor 8 for the feeding operation of the Y-axis (hereinafterreferred to as "Y-axis motor"). Further, a gantry 4 is mounted on theY-axis guide members 2 in such a manner as to be movable slidably alongthe Y-axis guide members 2 (that is, in the Y-direction) through arotational operation of ball thread 6 by the Y-axis motor 8. The Y-axisguide member 2, the gantry 4, the ball thread 6, and the Y-axis motor 8constitute a Y-axis feeding device 9.

Further, a pair of X-axis guide members 10 extending in the X-directionperpendicular to the Y-direction is fixedly mounted on the gantry 4, anda table 12 is mounted on the X-axis guide members 10 in such a manner asto be slidably movable along the X-axis guide members 10. On the gantry4 is rotatably mounted a ball thread 14, which is rotated by a servomotor 16 for the feeding operation of the X-axis (hereinafter referredto as "X-axis motor") to thereby move the table 12 in the X-direction.The X-axis guide member 10, the table 12, the ball thread 14, and theX-axis motor 16 constitute an X-axis feeding device 17. The Y-axis motor8 and the X-axis motor 16 are connected to rotational angle detectors 18and 20 for detecting respective rotational angles of the motors 8 and16. An object 22 to be machined is provided on the machine bed 1, and amachining head 24 is fixedly provided on the table 12.

Still further, an electronic control circuit 30 is provided to controlthe feeding operation of the feeding apparatus and perform a correctingoperation. The control circuit 30 includes a CPU 32 for performing anlogical operation, a ROM 34 serving as a memory means for storingcorrecting vectors, etc. as described below, a RAM 36 for temporarilystoring information and an input/output (I/O) port 38. These CPU 32, ROM34, RAM 36 and (I/O) port 38 are connected through a bus 40 to oneanother.

The I/O port 38 is connected to the Y-axis motor 8, the X-axis motor 16,and the rotational angle detectors 18 and 20, and further connected to anumerical position indicating device 46 comprising a key board 42 formanually inputting information on a feeding amount of each feeding axisby an user and so on, and a feeding program reader 44 for reading out anumerical information on the feeding operation which is stored in thememory beforehand and contained in an instruction tape or the like. Thenumerical position indicating device 46 outputs an instruction valuerepresenting a desired feeding position on the basis of theseinformations.

The CPU 32 is inputted through the I/O port 38 with the instructionvalue of the numerical position indicating device 46, detection signalsof the rotational angle detectors 18 and 20 and so on, and controls thefeeding operation of the Y-axis motor 8, the X-axis motor 16, etc. onthe basis of the above information, program and so on, therebyperforming its feeding control operation.

Next, a setting operation of the correcting vectors to be stored in theROM 34 will be described hereunder.

FIG. 3 is an explanatory diagram for showing a relationship between afeeding error and correcting vectors therefor when two linear feedingdevices are used.

As shown in FIG. 3, the feeding operation is conceptively shown by usinga two-dimensional feeding space compromising plural feeding axes orlines. In this case, it is assumed that X- and Y-axes which areperpendicular to each other are adopted as the feeding axes and thefeeding space comprises grid-patterned feeding lines. In FIG. 3, dottedlines represent an instructed feeding direction of the machining head 24along which the machining head 24 is instructed to be fed by an user ordata stored beforehand in the memory, and solid lines represent a realfeeding direction (locus) of the machining head 24 along which themachining head 24 is really fed without correction.

As shown in FIG. 3, two groups of dotted lines (hereinafter referred toas "X and Y instructed line groups") are assigned to the feeding space.The Y instructed line group comprises plural (m) dotted lines which arearranged in parallel with the Y-axis (direction) and at a predeterminedinterval (U) in the X-axis (direction), while the X instructed linegroup comprises plural (n) dotted lines which are arranged in parallelwith the X-axis (direction) and at a predetermined interval (V) in theY-axis (direction). These two groups of dotted lines are intersected toone another to form plural lattice points (hereinafter referred to as"instructed lattice points") at intersected points, which are used asrepresentative feeding points for feeding the machining head 24 to anyfeeding point (position). In the following description, the machininghead 24 is assumed to be fed in the feeding space.

In the feeding space, plural feeding areas Ai,j each of which issurrounded by four instructed lattice points NRi,j, NRi+1,j, NRi,j+1,andNRi+1,j+1 (i, j :any integer) are provided as shown in FIG. 3. Thenumber of these areas is (m-1)(n-1), and the machining head 24 is movedover these (m-1)(n-1) areas by Y-axis feeding device 9 and the X-axisfeeding device 17. The lattice intervals of U and V are beforehandstored in the ROM 34.

The CPU 32 outputs instruction values representing data on the X and Yinstructed line groups to the X- and Y-axes feeding devices 17 and 9 tothereby move the machining head 24 to a desired position, that is , toperform a positioning or feeding operation of the machining head 24.However, practically, the machining head 24 is not straightly moved inthe manner as instructed (along the dotted lines), and movedmeanderingly on the object 22 as represented by the solid lines if notsubjected to a feeding correction. This meandering line (or themeandering locus) is caused by not only a feeding error in theX-direction by the X-axis feeding device 17 and a feeding error in theY-direction by the Y-axis feeding device 9, but also combination amongan Abbe's error which is caused by the meandering of the Y-axis guidemember 2 on the XY plane, a feeding error in the X-axis direction by theY-axis feeding device 9, an Abbe's error which is caused by themeandering of the X-axis guide member 10 on the XY plane, an error inthe Y-axis direction, and an intersecting error between the X andY-axes. In the conventional feeding apparatus, only the former twoerrors have been corrected, while in this invention all of the aboveerrors can be completely corrected.

A space comprising these meandering lines (X and Y meandering lines) ishereinafter referred to as "machine feeding space", and the machinefeeding space includes plural lattice points at the intersecting pointsbetween the X and Y meandering lines. These lattice points of themachine feeding space is hereinafter referred to as "machine latticepoints.

When the X-axis and Y-axis feeding devices are moved on the basis of aninstruction value representing an instructed lattice point NRi,j, themachining head 24 is not really positioned at the instructed latticeposition NRi,j, but is really positioned at the machine lattice pointNi,j which is deviated from the instructed lattice point by eXi,j in theX-axis direction and eYi,j in the Y-axis direction. These deviationamounts of eXi,j and eYi,j correspond to feeding errors in the X-axisand Y-axis directions, respectively. In order to correct the feedingerrors, a correction vector Ei,j whose start and end points correspondto the machine lattice point Ni,j and the instructed lattice pointNRi,j, respectively, is newly introduced, and stored in correspondencewith an instruction value for each instructed lattice point. Thecorrection vector Ei,j is represented by the following equation (1), andrepresents both of a deviation amount and a deviation direction betweenthe machine lattice point Ni,j and the instructed lattice point NRi,j.

    Ei,j=(eXi,j eYi,j)                                         (1)

Here, eXi,j and eYi,j are correction amounts in the X-axis direction andthe Y-axis direction for the machine lattice point Ni,j, respectively.Further, the correction vectors for the machine lattice points over allthe feeding areas are represented by the following matrix (2). ##EQU1##

This correction matrix is beforehand measured and stored in the memory,and used to obtain a correction vector for any desired feeding position.

The correction amount eXi,j of the correction vector Ei,j serves tocorrect not only the feeding error (eiX) of the X-axis feeding device 17in the X-axis direction, but also the Abbe's error due to the meanderingof the Y-axis guide member 2 on the XY plane and the feeding error inthe X-axis direction which is caused by the Y-axis feeding device 9.Likewise, the correction amount eYi,j of the correction vector Ei,jserves to correct not only the feeding error (ejY) of the Y-axis feedingdevice 9 in the Y-axis direction, but also the Abbe's error due to themeandering of the X-axis guide member 10 on the XY plane and the feedingerror in the X-axis direction which is caused by the Y-axis feedingdevice 17.

An arithmetic operation of the CPU 32 for obtaining correction vectorsfor any points in the feeding areas will be hereunder described withreference to FIG. 4.

FIG. 4 is a partly-enlarged view of the feeding areas as shown in FIG.3. A correction vector at any point Nx,y in the feeding areas can becalculated using four correction vectors for four instructed latticepoints of a feeding area to which the point Nx,y belongs. For example,assuming that the point Nx,y belongs to the feeding area Ai,j, thecorrection vectors for the instructed lattice points NRi,j, NRi+1,j,NRi,j+1 and NRi+1,j+1 of the feeding area Ai,j including the point Nx,yare represented by Ei,j, Ei+1,j, Ei,j+1, and Ei+1,j+1, and Δ X and Δ Yrepresent distances in the X-axis and Y-axis directions between theinstructed lattice point NRi,j and the point Nx,y, respectively, thecorrection vector Ex,y for the point Nx,y which is numerically inputfrom the numerical position indicating device 46 is interpolativelycalculated and represented by the following equation (3) ##EQU2##

When the point Nx,y is consistent with the instructed lattice pointNRi,j, the correction vector Ei,j for the point NRi,j 1 is one for thepoint Nx,y. When the point Nx,y is not consistent with the instructedlattice point NRi,j, a correction vector for any point can beinterpolatively calculated using the correction vectors Ei,j, Ei+1,j,Ei,j+1 and Ei+1,j+1 for the four instructed lattice points NRi,j,NRi+1,j, NRi,j+1 and NRi+1,j+1 with high accuracy.

The above description is made to the arithmetic operation of thecorrection vectors for the two-dimensional feeding space. However, thesimilar arithmetic operation can be also applied to higher-dismensionalfeeding spaces than the two-dimensional feeding space. For example, whena three-dimensional orthogonal feeding space is introduced using X-axis,Y-axis and Z-axis feeding devices, all correction vectors Ei,j,k for allinstructed lattice points in the three-dimensional feeding space whichare represented by the following equation (6) are beforehand stored inthe ROM 34. The correction vector matrix P for all the instructedlattice points is represented by the following equation (7).

    Ei,j,k=(eXi,j,k eYi,j,k eZi,j,k)                           (6)

    P=(Ei,j,k), 1≦i≦m, 1≦j≦n, 1≦k≦0(7)

A correction vector Ex,y,z for any point Nx,y,z is represented by thefollowing equation (8) using the equations (6) and (7). ##EQU3##

Here, α=ΔX/U (9), β=ΔY/V (10), γ=ΔZ/W (11) U, V and W represent latticeintervals in the X, y and Z directions, respectively.

FIG. 5 is a block diagram for showing an embodiment of the correctingdevice used in the numerically controlled feeding apparatus according tothis invention.

The correcting device as shown in FIG. 5 includes at least two linearfeeding devices Ml for linearly feeding the machining head in directionsintersected to each other, a memory means for storing correction vectorsbeforehand each of which represents deviation amount between aninstructed lattice point and a machine lattice point correspondingthereto, a numerical position indicating device M2 for outputting aninstruction value representing a desired position at which the machininghead is fed, and a feeding amount control means M4 for receiving theinstruction value from the numerical instruction device M2 to feed themachining head to the position represented by the instruction value, andcalculating a corrected feeding amount on the basis of the instructionvalue and the correct (on vector stored in the memory means M3 to feedthe machining head by the corrected feeding amount and dispose it to thedesired position.

A control processing of a feeding operation by the control circuit 30will be next described hereunder in accordance with a flowchart as shownin FIG. 6, particularly in a case where the two-dimensional feedingspace is adopted.

Upon output of an instruction value representing a desired feedingposition Nx,y from the numerical position indicating device 46, fourcorrection vectors Ei,j, Ei+1,j, Ei,j+1, and Ei+1,j+1 for fourinstructed lattice points NRi,j, NRi+1,j, NRi,j+1 and NRi+1,j+1 in afeeding area Ai,j which includes the position Nx,y, and the latticeintervals U and V are read out of the ROM 34 serving as the memory meansM3 (step S110). Thereafter, coefficients α and β are calculated by theequations (4) and (5), and a correction vector Ex,y for the positionNx,y corresponding to the instruction value is calculated by theequation (3) (step S120).

The correction vector Ex,y thus calculated is added to the instructionvalue to obtain a corrected feeding amount (step S130). Thereafter, theY-axis motor 8 and the X-axis motor 16 is controlled to move themachining head 24 by the corrected feeding amount and dispose it to theposition Nx,y on the object 22 while rotational angles of the Y-axismotor 8 and the X-axis motor 16 are detected by the rotational angledetectors 18 and 20, respectively, and detection signals of thedetectors 18 and 20 are fed back (step S140).

According to the numerically controlled feeding apparatus of thisinvention, correction vectors Ei,j whose start and end points correspondto machine and instructed lattice points Ni,j and NRi,j are measuredbeforehand and determined for all instruction values corresponding toall instructed lattice points NRi,j. Thereafter, any correction vectorEx,y for any instruction value indicating any feeding point Nx,y whichis outputted from the numerical position indicating device 46 iscalculated on the basis of the following eight parameters: fourcorrection vectors Ei,j, Ei+1,j, Ei,j+1 and Ei+1,j+1 for four instructedlattice points NRi,j, NRi+1,j, NRi,j+1 and NRi+1,j+1 at a feeding areaAi,j including the point Nx,y, distances (deviations) x and y in theX-axis and Y-axis directions between the instructed lattice point NRi,jand the feeding point Nx,y, indicated by the instruction value, and theintervals U and V of the feeding space. The calculated correction vectorEx,y is added to the instruction value to obtain a corrected feedingamount and then the X-axis and Y-axis motors 8 and 16 are controlled onthe basis of the corrected feeding amount. Accordingly, the correctionamount(component) eXi,j in the X-axis direction of the correction vectorEi,j for the instructed lattice point Ni,j covers not only feeding errorε iX in the X-axis direction by the X-axis feeding device 17, but alsoanother feeding error ε iY in the X-axis direction by the Y-axis feedingdevice 9. Likewise, the correction amount(component) eYi,j in the Y-axisdirection of the correction vector Ei,j for the instructed lattice pointNi,j covers not only feeding error ε jY in the Y-axis direction by theY-axis feeding device 9, but also another feeding error ε jX in theX-axis direction by the Y-axis feeding device 17. Therefore, not onlyauto-feeding errors of the X-axis and Y-axis feeding devices 17 and 9,respectively, but also a correlative feeding error between these feedingdevices 17 and 9 can be corrected to thereby perform a correctingoperation with high accuracy, so that feeding and positioning controlsare carried out with high accuracy.

This invention is not limited to the above embodiment, and anymodification may be made to the embodiment without departing from thesubject matter of this invention. For example, the above embodiment wasdescribed for the two-dimensional feeding apparatus, however, thisinvention may be applied to a higher-dimensional feeding apparatus.Further, this invention may be applied not only to an intermittentpositioning control for merely performing a positioning operationbetween at least two points, but also performing a continuouspositioning control of a specific locus (outline) between the points ata predetermined rate. In this case, the locus (outline) is divided intoplural fine vectors and then each vector is subjected to a correctingoperation.

What is claimed is:
 1. A numerically controlled feeding apparatus havingat least two linear feeding devices having intersected feedingdirections for performing a numerical feeding control in a feedign spacedefining a plurality of feeding areas on the basis of an instructionvalue representing a desired feeding position, comprising:memory meansfor storing representative correction vectors for representativeinstruction values indicating a predetermined number of referencefeeding positions in the feeding space, each representative correctionvector having information on deviation amount and deviation directionbetween a reference feeding position indicated by each of therepresentative instruction values and a real feeding positioncorresponding to each of the representative instruction values, thedeviation amount and deviation direction being indicative of an error ofeach said linear feeding device caused by at least one component of afeeding error of the other feeding devices; correcting means forcalculating a correction vector for an instruction value indicating anydesired feeding position on the basis of a correction vector group ofrepresentative correction vectors for representative instruction valuesindicating plural feeding positions located in adjacent feeding areas ofthe desired feeding position, the correction vector group being read outof said memory means, and the instruction value indicating the desiredfeeding position, thereby to obtain a corrected feeding amount; andcontrol means for controlling a feeding operation of said linear feedingdevices on the basis of the corrected feeding amount.
 2. The numericallycontrolled feeding apparatus as claimed in claim 1, wherein saidreference feeding positions correspond to cross points between two linegroups including predetermined numbers of lines in parallel with theintersected feeding directions, respectively.
 3. The numericallycontrolled feeding apparatus as claimed in claim 2, wherein said twoline groups comprise a grid pattern.
 4. The numerically controlledfeeding apparatus as claimed in claim 1, further comprising feedingamount detecting means for detecting feeding amounts of said linearfeeding devices to output a detection result to said control means tothereby perform the feeding operation with feedback.
 5. The numericallycontrolled feeding apparatus as claimed in claim 1, wherein each of saidlinear feeding devices comprises a ball thread and a servo motor forrotating said ball thread.
 6. The numerically controlled feedingapparatus as claimed in claim 5, further comprising rotational angledetecting means for detecting a rotational angle of said servo motor tothereby detect a feeding amount of each of said linear feeding devices.7. A method for performing a feeding operation of a numericallycontrolled feeding apparatus having at least two linear feeding deviceswhile correcting a feeding error, comprising the steps of:measuring andstoring representative correction vectors for representative instructionvalues indicating a predetermined number of reference feeding positionsin a feeding space defining a plurality of feeding areas, eachrepresentative correction vector having information on deviation amountand deviation direction between a reference feeding position indicatedby each of the representative instruction values and a real feedingposition corresponding to each of the representative instruction values,the deviation amount and deviation direction being indicative of anerror of each said linear feeding device caused by at least onecomponent of a feeding error of the other feeding devices; calculating acorrection vector for an instruction value indicating any desiredfeeding position on the basis of a correction vector group ofrepresentative correction vectors for representative instruction valuesindicating plural feeding positions located in adjacent feeding areas ofthe desired feeding position, and the instruction value indicating thedesired feeding position, thereby to obtain a corrected feeding amount;and controlling a feeding operation of the lienar feeding devices on thebasis of the corrected feeding amount.